The structure of quasi-shocks in a collision-free plasma in a magnetic field

1967 ◽  
Vol 1 (1) ◽  
pp. 129-144 ◽  
Author(s):  
J. G. Cordey ◽  
P. G. Saffman
Keyword(s):  
Magnetic Field ◽  
Finite Amplitude ◽  
Mean Values ◽  
Turbulent Transition ◽  
Random Manner ◽  
Flow Through ◽  
Steady Solutions ◽  
Flow Variables ◽  
Hydromagnetic Waves ◽  
Free Plasma

A study is made of finite amplitude, oblique, hydromagnetic waves in a cold collision-free plasma. It is shown that the equations admit steady solutions which describe flow through a front. Ahead of the front, the flow is uniform, but behind the front the magnetic field and flow variables oscillate irregularly in a random manner. The fronts are called ‘quasi-shocks’, although they have more in common with the laminar-turbulent transition of fluid mechanics than with the classical shock wave. The structure of the quasi-shocks is examined, and estimates are made for the mean values behind the front. The relevance of the quasishocks to the so-called ‘collision-free shock’ is considered, and comparison is made with the ‘bow shock’ on the solar wind near the earth. It is shown that the quasi-shock is consistent with some of the observed data.

scholarly journals Propagation of a solitary wave along a magnetic field in a cold collision-free plasma

1961 ◽  
Vol 11 (1) ◽  
pp. 16-20 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Magnetic Field ◽  
Geometric Mean ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Order Of Magnitude ◽  
Hydromagnetic Waves ◽  
Cold Collision ◽  
The Magnetic Field ◽  
Free Plasma ◽  
Alfven Velocity

It is shown that solitary hydromagnetic waves can propagate parallel to a uniform magnetic field in a cold collision-free plasma. These waves are exact solutions of the non-linear equations of motion except for the quasi-neutral approximation. The velocity of propagation lies in a range of values somewhat larger than the Alfvén velocity, and is of the order of 25 times the Alfvén velocity for hydrogen, the precise value depending upon the strength of the wave. Simple expressions exist for the velocities of the ions and electrons and the magnetic field inside the wave. The lines of force are spirals about the direction of propagation. The waves are symmetrical about their middle. The order of magnitude of their width is the geometric mean of the gyro-radii of the ions and electrons when moving with the Alfvén velocity. The maximum value of the magnetic field can be somewhat larger than the value away from the wave.

On the modulational instability of hydromagnetic waves parallel to the magnetic field

1976 ◽  
Vol 16 (3) ◽  
pp. 321-334 ◽  
Author(s):  
Einar Mjølhus
Keyword(s):  
Magnetic Field ◽  
Stability Condition ◽  
Modulational Instability ◽  
Finite Amplitude ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Arbitrary Amplitude ◽  
The Stability ◽  
Hydromagnetic Waves ◽  
The Magnetic Field

The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.

Stability of axially symmetric flow driven by a rotating magnetic field in a cylindrical cavity

2001 ◽  
Vol 431 ◽  
pp. 407-426 ◽  
Author(s):  
I. GRANTS ◽  
G. GERBETH
Keyword(s):  
Magnetic Field ◽  
Metal Flow ◽  
Finite Amplitude ◽  
Rotating Magnetic Field ◽  
Axially Symmetric ◽  
Stable Regime ◽  
Görtler Vortices ◽  
Gortler Vortices ◽  
Steady Solutions ◽  
The Stability

This paper deals with the stability analysis of an axially symmetric liquid metal flow driven by a rotating magnetic field in a cylinder of finite dimensions. The limit of linear stability with respect to axially symmetric perturbations is found for diameter-to-height ratios between 0.4 and 1. This oscillatory instability is shown to be different from the expected Taylor–Görtler vortices. Several linearly unstable steady solutions are found close to the stable basic state. It is shown that small finite-amplitude perturbations in the form of Taylor–Görtler vortices give rise to instability in the linearly stable regime.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

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